In order to get as much information as possible about the properties of a formation surrounding a borehole, modern sonic-logging technology has developed over the last few decades. For example, an acoustic source or a transmitter, e.g., a monopole, dipole, quadrupole, etc. source, emits an acoustic wave inside the borehole. The resulting acoustic wave is then recorded with an acoustic array after it has reached the borehole walls and traveled through the formation via elastic waves. Data analysis on the recorded waveforms provides useful information about the geophysical properties of the borehole. Such information is composed of the slowness of the different types of waves traveling through the formation, as well as the dispersion curves when the slowness is frequency dependent.
Sonic tools have been designed in order to operate simultaneously with the drilling of the borehole. Such tools are called logging-while-drilling (“LWD”) tools and are linked to a bit within a bottom hole assembly (“BHA”). Processing sonic data obtained from LWD is a challenging task because the recorded waveforms experience a low signal to noise ratio (“SNR”) due to the drilling noise, for example, any noise generated by the drilling operation such as the sound of the bit grinding the rock and/or any shocks of the BHA against the borehole walls. The noisy data acquired by LWD sonic logging requires robust techniques to extract useful information.